The ghost of Ilya Shpitser will glower at you for conditioning directly on bet, rather than on the counterfactual where you take the bet. But I’d like to see where you go before hammering on that point.
If I understand you, these are the expected values of the utility functions you outline.
Event | u | T |u + T
------------+------+------+-----
no bet | $49 | $0 | $49
bet | $50 | $0 | $50
bet & heads | $0 | $50 | $50
bet & tails | $100 | -$50 | $50
The ghost of Ilya Shpitser will glower at you for conditioning directly on bet, rather than on the counterfactual where you take the bet. But I’d like to see where you go before hammering on that point.
If I understand you, these are the expected values of the utility functions you outline.
Is that correct?
Yes, I was not looking at subtleties like that :-)
Your table is correct.
EDIT: your table is correct, but there are some extra unimportant subtleties—like the fact that under “bet”, you don’t have a u, only an expected u.